In earlier papers, the authors have presented theoretical and experimental results for the generation of focused surface wave motion by a linear array of surface wave transducers. It was shown that a single element generates a beam with an opening angle of approximately 20°, and a cross section which can be accurately represented by a Gaussian distribution of the normal displacements. For an eight-element array, the focused beam was modeled by superposition considerations. Comparisons of theoretical and experimental results, where the latter were obtained by the use of a laser interferometer, showed excellent agreement for the normal displacement both along a radial line and across the width of the beam. The transducer array with a center frequency of 5MHz was used for surface-defect detection, whereby the focal region was automatically adjusted to the defect location. In this paper the results of [1]-[4] are used to construct a measurement model for the ultrasonic measurement of the signal backscattered from a surface-breaking crack. The signal scattered back from the defect has been expressed in terms of a scattering coefficient based on the use of an elastodynamic reciprocity relation, originally developed by Auld and Kino. The Kirchhoff approximation was used to compute the scattering coefficient for the experimental configuration. This approximation can be applied if the defects are considerably larger than the ultrasonic wavelength, and if the angle between incident field and backscattered field is small. A simplification of the mathematical description was achieved by using the plane-wave reflection coefficient for a surface wave derived by Achenbach et al. and Gautesen.
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